The
time it takes a home building company to build a new home is directly
proportional to the size of the home and inversely proportional to
the number of people on the building crew. If it takes 10 workers 4
weeks to build a 2,000 square foot home, how long will it take 6
workers to build the home?

**Solution:**

Let

*t*= time it takes to build a home*w*= number of workers

*s*= size of home

The
joint variation between these variables can be represented by

*t = ks/w*

Substitute
4 for

*t*, 2000 for*s*and 10 for*w*and solve for*k.*
4 =

*k*(2000)/10
Multiply
both sides by 10 to clear the denominator.

40
=

*k*(2000)
Divide
by 2000 to get

40/2000
= 1/50 =

*k*.
Now
substitute 6 for

*w*, 2000 for*s*and 1/50 for*k*and solve for*t*.*t*= (1/50)(2000/6)

*t*= 2000/300,

*t*= 6.66. Therefore, it takes 6 workers 6 2/3 weeks to build a 2,000 square foot home.

## No comments:

## Post a Comment